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The human visual system is confronted with a basic problem when representing space in that large amounts of memory are required. One solution would be to have sufficient processing to represent all visual features at every location; however, this is probably neither possible nor necessary. We argue that a polyhedral model of extrapersonal space can be built up sequentially over a series of fixations using a channeled input. The parametric representation of the space allows the visual system to maximize the usefulness of the data at any fixation. Furthermore, once the data structure is built up, it can be used in parallel for various tasks requiring spatial planning. The sparse nature of the data in spatial memory means that it can be economically represented with coarse coding. Coarse coding's disadvantages can be alleviated in this case by using focusing mechanisms.